I don't think anyone can claim to have 'invented' a patch of decorative grass as such, but a commonly cited example is Louis XIV's expansion of the Palace of Versailles out of marshland and surrounding it with decorative gardens containing 'tapis vert'- green carpet. Clearly owning land which takes effort to keep decorative (pre-lawnmowers this would have been a laborious task) is going to be the reserve of the wealthy, but it's when you get into landscaping through the 17th & 18th Centuries that decorative gardens really take off into the realms of an art form- shaping the land to create specific effects (none with actual uses), using techniques pioneered in the Netherlands, and styles popularised in Britain.

It's not an entirely uselss crop. -At least not originally. In the past, largish plots of grass were used to graze goats or sheep who would, in turn, also keep it mowed. Central park was even used and maintained in this way. A herd of sheep or goats can keep grass trimmed very short and tidy.